Spiderweb honeycombs

Small and large deformation in-plane elastic response of a new class of hierarchical fractal-like honeycombs inspired by the topology of the ''spiderweb'' were investigated through analytical modeling, detailed numerical simulations, and mechanical testing. Small deformation elasticity results show that the isotropic in-plane elastic moduli (Young's modulus and Poisson's ratio) of the structures are controlled by dimension ratios in the hierarchical pattern of spiderweb, and the response can vary from bending to stretching dominated. In large deformations, spiderweb hierarchy postpones the onset of instability compared to stretching dominated triangular honeycomb (which is indeed a special case of the proposed spiderweb honeycomb), and exhibits hardening behavior due to geometrical nonlinearity. Furthermore, simple geometrical arguments were obtained for large deformation Poisson's ratio of first order spiderweb honeycombs, which show good agreement with numerical and experimental results. Spiderweb honeycombs exhibit auxetic behavior depending on the non-dimensional geometrical ratio of spiderweb. The spider's web is a highly efficient network of natural fibers where the geometry plays a major role in unique properties such as significant strength, toughness and reversible extensibility. From the structural point of view, the current state of literature on the spiderweb includes evaluation of the elastic properties of spider silk (Blackledge et al. and the out-of-plane mechanical properties of the structure under various static, dynamic, and impact loadings produced by wind, insects, or other natural In the current paper we incorporate the spider-web structural organization into hexagonal honeycombs resulting in a centrosymmetrical fractal-like pattern. Recently, it has been shown that engineered self-similarity can be exploited to control the mechanical properties of cellular struc-out a comprehensive study of hierarchical design which considered multiple parameter enhancements of high order hierarchical honeycomb lattices and showed that remarkably favorable combinations of specific stiffness and specific strengths can be simultaneously achieved via hierarchical organization. However, unlike previously introduced geometries, the current topology has the advantage of controlling the response through a critical transition between two main structural responses in a cellular solid, namely the stretching and bending dominated behaviors. The transverse (i.e. in-plane) elastic modulus of a regular hexagonal honeycomb is governed mostly by the bending deformation of cell walls and is related to the structure's relative density through the closed-form expression: E=E s ¼ 1:5q 3 , where E and E s are respectively the Young's moduli of the structure and cell wall material, and q is the relative density of the structure (Gibson and Ashby, …